Mathematics for ELL Students Workshop 1 Presentation

Teaching High-Level Mathematics to English Language Learners

in the Middle Grades

1135 Tremont Street, Suite 490Boston MA 02120

© Copyright 2009 Center for Collaborative Education/Turning Points

Workshop 1

Teaching High-Level Mathematics to English Language Learners in the Middle Grades was developed by Turning Points, a project at the Center for Collaborative Education in Boston, MA. This tool is part of the Mathematics Improvement Toolkit, a project of the National Forum to Accelerate Middle Grades Reform, and was supported by the U.S. Department of Education’s Comprehensive School Reform Initiative, grant #S332B060005. Opinions expressed are those of the authors and are not necessarily those of the Department.

Developed byTurning Points, a project of

the Center for Collaborative Education

WELCOME!

✎WRITE ➔

Write your name on a name-tag with the markers on the table (if you don’t already know everyone in the workshop).

TAKE ➔

Please take a participant’s packet if you haven’t already taken one.

BEST PRACTICE: VISUAL CUESEasy-to-identify, visual cues •call attention to key points and critical classroom routines,

•reduce the language load,

•create predictable and easy-to-follow routines, and

•allow English language learners to participate quickly and actively in lesson.

Workshop 1 Agenda

• Challenges Facing English Language Learners: The Language of Mathematics

• Introductions/Creating Community/Prior Knowledge

• Classroom Video #1

• Framing Principles of Tool

• English Language Learners: Who are they today?

• Challenges Facing English Language Learners: Word Problems

• Word Problems: Creating Supports for English Language Learners

• Classroom Videos: #2, #3, and #4

• Action Plans: Next Steps in the Classroom

• Closing/Reflections/Feedback

1-1

Workshop 1

Teaching High-Level Mathematics to English Language Learners in the Middle Grades

Overview of Workshop

Series




In workshop 1, you will learn:• who the English language learners in schools are today• how to recognize some of the challenges faced by English language learners in learning high-level mathematics• how to support English language learners in learning the language of mathematics• how to ensure the active engagement of English language learners in developing the mathematical reasoning essential to mastering high-level mathematics.In workshop 2, you will learn:• how to distinguish high-level from low-level mathematical tasks in the middle grades• how to create high-level math activities that engage English language learners in the middle grades.

1-2



The Research Base

Think

✎Write

Pair

Share

BEST PRACTICE: DISCUSSION PROTOCOLDiscussion protocols are designed

•to provide clear guidelines and expectations for class discussions that are accessible to all students,

•to ensure that English language learners have the time they need to process what they hear and formulate their ideas in a new language,

•to make sure that all students, including English language learners, are equal contributors to the discussion as speakers and listeners, and

•to allow for alternative ways of thinking to be aired and evaluated.

1-3A

Think

Think about something in your own background that can be or has already been helpful in teaching mathematics to English language learners.

BEST PRACTICE: USING PRIOR KNOWLEDGE AS A LINK TO NEW KNOWLEDGE•Prior knowledge gives English language learners entry points to every lesson•All “big ideas” in mathematics can be linked to the prior knowledge of all English language learners•Open ended, higher order thinking questions are excellent ways of accessing this knowledge

1-3B

Write

WRITE your response down, using ONLY ONE SYLLABLE words. ✎

Next, describe the same response using a different modality - drawing, acting out, creating a chart or map. Use as few words as possible.

drawing map chart

1-3B

1-3C

PairTake turns sharing your responses with a partner.

Shareyour responses with the larger group.

What did you learn from this exercise that you will keep in mind when you teach mathematics to English language learners?

What questions did this exercise raise for you about teaching high-level mathematics to English language learners?

1-4

All of these protocols and strategies model the use of best instructional practices for teaching high-level mathematics to all students, including English language learners.

THINK WRITE PAIR SHAREis the first of many protocols and strategies we will use throughout the workshop.

You will see and hear a broad range of English language learners (those who are in the first stages of learning English and those who are in more advanced stages) using them during these workshops.

• mathematical reasoning,

•understanding and using the language of math,

• the search for alternative ways to solve problems,

• the ability to explain and defend solutions, and

• the use of pictures, diagrams and symbols to make these strategies accessible to English language learners.

The best instructional strategies in mathematics promote

Why do you think this is so?

English language learners are rarely exposed to these strategies in the middle grades.

THINK PAIR SHAREWRITE

The workshop will introduce THINK WRITE PAIR SHARE and others that were specifically developed for English language learners.

As participants, you will have an opportunity to master the use of all of these strategies.

What does it look like and sound like when English language learners use

these best instructional strategies?

The video captures the first time they are using the protocol to discuss a mathematical concept.

Video of English language learners learning to use a discussion protocol.

What does it look like and sound like when English language learners use

these best instructional strategies?

The SchoolUrban school15% English language learners

The Class7th grade class, 40% ELLs23 students in the class

The TeacherHas taught for 3 yearsTeaches without in-class supportFirst time she has used this protocol in her

teaching

The English language learnersEnglish language learners have lived in United States between one and

two yearsMathematics is the only subject that the English language learners in this

classroom are placed with native speakers of EnglishEnglish language learners rarely spoke in math class until discussion

protocols were introduced

1. The teacher reminds them of the work they had done the previous day. She introduced •a discussion protocol and•sentence frames or “Say something” - pattern language students could use in responding to each other.

BEST PRACTICESAY SOMETHING

SEQUENCE of CLIPS

The students have a handout of the sentence starters on their desk. The teacher also posts them on a chart in the front of the classroom.

2. Each student in the class individually works on a set of problems to determine if shapes are similar or not similar. This is review work for the students, and the teacher chose it so that the students would only have to handle one new learning at a time - in this case, the discussion protocol.

3. A group of three English language learners hold a discussion about whether the shapes are similar or not similar and why.

This is the first time they have used the protocol. They had practiced using the sentence starters in the previous lesson.

BEST PRACTICE: INTRODUCE ONE NEW LEARNING AT A TIME•students are better able to concentrate when they are learning one skill at a time•use simple, already mastered work when introducing a new procedure or strategy•English language learners feel ready to learn a new skill when they are learning it with material they feel confident they already know

1-5

how the teacher structures the lesson to encourage discussion among all students

how the English language learners use language to talk about the mathematical concepts in the lesson

Using Handout 1-6, take notes on

1-6

Video #1

1-7

PAIR Discuss with a partner



SHARE some of the responses you heard with the larger group.

The Framing Principles of Teaching High-Level Mathematics

to English Language Learners in the Middle Grades

The Framing Principles of the Turning Points Tool

English language learners have a right to learn high-level mathematics in the middle grades.

English language learners should move forward with their conceptual math growth, while simultaneously accelerating their skills in number sense and numerical skills.

English language learners learn best in a school-wide and classroom culture of high expectations.

English language learners have a deep and broad range of prior knowledge that links directly to the critical concepts of middle grades mathematics. This prior knowledge can be used as a important resource to support the learning of all students.

1-8A

The Framing Principles (continued)

The best instructional practices for teaching high-level mathematics to all learners are the best practices for English language learners.

English language learners need additional support that is uniquely designed to meet their linguistic and cultural backgrounds in learning high-level mathematics.

English language learners need to speak and listen to others throughout their math classes in order to master the mathematical reasoning of high-level mathematics.

English language learners must learn the language of mathematics to explain how they solved a problem and why they took the steps they took.

English language learners may use their native language as a needed support when they are first learning a concept, while at the same time developing their fluency in using the language of math in English.

1-8B

The Framing Principles (continued)

PAIR/SHAREChoose one of the principles to discuss with a partner.

Use one of the sentence frames below to structure your responses.

BEST PRACTICE: SENTENCE FRAMES/PATTERN LANGUAGE•provide a clear scaffold for English language learners which they can use to participate in discussions•are practiced with students before they are asked to use them individually•allow students to have some choice in their responses•encourage higher order thinking.

I have chosen the principle that says ....... because........Have you always thought that way? Why? Why not?

I noticed that ...... One example might be....I agree/disagree because....

Who are the English language learners in our schools today?

English language learners are the fastest growing segment of the school population. 1 out of 10 students enrolled in public schools is an English language learner. *

English language learners are expected to be 30% of the school age population by 2015.

Nearly 1 out of 3 students enrolled in urban schools is an English language learner.

The percentage of English language learners enrolled in schools is increasing throughout the United States, in suburban, rural as well as urban communities.

* see handouts for citations of all statistics presented in workshop

1-9A


*

I notice that...

SPEAK

It is important because...

RESPONDRESPOND

I agree because ....I disagree because...

What else do you notice?Why do you think that is important?

FOLLOW UP QUESTION

1-9A

BEST PRACTICE: RESPONSE/FOLLOW-UP QUESTION/RESPONSE• gives English language learners several opportunities to use the language of mathematics• models a typical discussion for English language learners• encourages students to go deeper in understanding the problem• provides pattern language as entry points for English language learners

Take turns analyzing the map with a partner.

Sources: U.S. Department of Education’s Survey of the States’ Limited English Proficient Students and Available Educational Programs and Services, 1991-1992 through 2000-2001 summary reports; state publications (1998-1999 data); enrollment totals from the National Center for Educational Statistics Core of Common Data, 1998-1999


Share What were some of the interesting things you or your partner noticed when you analyzed the map?

We noticed that..... We thought that was interesting because...

English language learners enroll in schools speaking many different languages.


The great majority in the United States as a whole are native speakers of Spanish.

English language learners have a strong desire to receive an education. They have the highest daily attendance rate of any segment of the school population.

English language learners have the lowest out of school suspension rates of any segment of the school population.

However,

English language learners have the lowest standardized test scores of any segment of the school population.

English language learners have the highest dropout rate of any segment of the school population.

What do we know about their experience in our schools?

Why do you think this is so?

THINK PAIR SHAREWRITE

1-10A

1-10B

Challenges Facing English Language Learners

Please read “Learning the Language of Mathematics in the Middle Grades: The Specific Challenges for English Language Learners.”

Mark one important idea you want to discuss with your group. Be prepared to tell the group why you think this particular idea is important.

1-11A,B

Get into groups of three.

Choose a timekeeper.

We will now model and practice another small group discussion protocol. It is designed to provide an opportunity for English language learners to discuss and rehearse their ideas with others in small groups before they share them with the larger group.

No one else speaks during the entire minute.

The first person reads excerpt to the group, then has one minute to discuss the excerpt.

BEST PRACTICE: FINAL WORD• efficient way to discuss a reading• provides controlled choice• makes sure all voices are heard• ensures in-depth discussion of issues important to group• provides entry point into discussion for those who have not been able to read or absorb entire document• English language learners can choose the part of the text they understand best.

We will use THE FINAL WORD.

The next person in the group responds for one minute.

Continue until everyone has had a chance to start and end the discussion.

When everyone else has spoken, the first person has one minute for THE FINAL WORD.

No one else speaks during that minute.

In the next exercise, we will be working with word problems.

SHARE After reading the article and hearing the discussion, what kinds of challenges do you think English language learners might face in reading, interpreting and solving word problems?

Looking at Word Problems: The Challenges for English Language Learners

Let’s look at a word problem.

What specific challenges do you think an English language learner in the middle grades might have in trying to answer the question posed by the problem?

(Notice that you are not solving the problem; instead you are analyzing the difficulties raised for a diverse group of English language learners as they approach the problem.)

A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job?

1) What are some language challenges in this problem for English language learners?

THINK

2) What are some math challenges in this problem for English language learners?

3) What are some cultural challenges that could cause difficulty in understanding this problem for English language learners?


WRITE1-12


WRITE Use Handout 1-13 to record your responses.

BEST PRACTICE: PROVIDING an ORGANIZING TEMPLATE/GRAPHIC ORGANIZER•saves time•focuses English language learners’ attention on the mathematical concepts rather than copying in a new language• models how to organize information•provides clear way students can organize information•creates expectations about # and quality of responses

What are the language challenges in this problem for English language learners?

What are the math challenges in this problem for English language learners?

What are the cultural challenges that could cause difficulty in understanding this problem for English language learners?

1)

2)

3)

4)

1)

2)

3)

4)

1)

2)

3)

4)

1-13

Get into groups of four. Assign one person to chart the responses to the first question, one at a time. Take turns listening to each others’ responses.

GROUP A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job?

As each person speaks, ask any questions or make comments that help expand their comments further.

What are the language challenges in this problem for English language learners?

#1

#3#4

#2➟

➟

➟

#1

#2

#4 #3

➟

➟

➟

Small Group discussion

Assign number 1, 2, 3 or 4 to each member of your group. If you hear your number (1,2,3 or 4), please share two of your group’s responses about the language challenges.

SHARE

#4

#4

Share out to class

#1

#1

All #1s SHARE

All #4s SHARE

BEST PRACTICE: NUMBERED HEADS ASSESSMENT STRATEGY•encourages all students to hold each other accountable•encourages all students to collaborate in creating a thoughtful and thorough response•ensures that all students are given a chance to respond publicly•efficient way to check for understanding with entire class and immediately address misconceptions and misunderstandings

Get into groups of four. Assign one person to chart the responses to the second question, one at a time. Take turns listening to each others’ responses.



What are the mathematical challenges in this problem for English language learners?

Please share two of your group’s responses about the mathematical challenges.

SHARE

All #2s SHARE Share

out to class

All #3s SHARE

#3#3

#2

#2

Get into groups of four. Assign one person to chart the responses to the third question, one at a time. Take turns listening to each others’ responses.



What are the cultural challenges in this problem for English language learners?

Please share two of your group’s responses about the cultural challenges.

SHARE

#4

#4

Share out to class

All #2s SHARE

All #4s SHARE

#2

#2

READ/COMPARE

Discuss in rounds: How is this list similar and different from the one we have generated?

Divide into three groups and take out Handouts 1-14 A,B,C,D and E .

Each group will read one challenge area (language, mathematical or cultural) presented by the word problem.

SHARE

Use Numbered Heads to share out to entire group.

1-14A,B,C,D,E

Working on Word Problems: Supports for English Language Learners

•How does this lesson ensure that English language learners are engaged in high-level mathematics: 1.solving challenging problems, 2.using mathematical reasoning, and•explaining their thinking?

•How does this lesson ensure that all English language learners are engaged at all times throughout the lesson?

•How does this lesson support English language learners learning mathematics in the middle grades •without simplifying the problem, •telling them what to do, or •telling them the answer?

Three Essential Lesson Planning Questions

1-15A

One important type of support is scaffolding.

We have analyzed many of the challenges that English language learners will face in solving the word problem.

What supports can we provide to help them overcome these challenges?

Scaffolding: a process of ‘setting up’ the situation to make the child’s entry easy and successful and then gradually pulling back and handing the role to the child as he becomes skilled enough to manage it. (Bruner, 1983: 60)

Scaffolding does not lower the cognitive demand for students; it provides

• just the right rich mathematical activities, tools, directions and questions • at just the right time

so that the students are able to continue to tackle the new challenge -

• without being told the steps they should take to solve the problem and • without being given the answers.

What kind of support would help English language learners solve the problem without lowering its

cognitive demand? 1-15B

BEST PRACTICE:•Using prior knowledge to connect to new concept•Discussion protocols•Think/write/pair/share•Assigning numbers for round robin discussion•Visual cues•Sentence frames•Speak/respond/ question/respond•Organizing template•Numbered heads•Final word•One new learning at a time

Now look back on the list of challenges.

Consider different kinds of supports and scaffolds to address those challenges, such as:

concretekinestheticlinguisticgraphic organizers

The objective is to “set up” a situation and create a lesson plan so that the process of learning is easy and successful for English language learners, while at the same time having a high cognitive demand. Think back on some of the best practices used earlier in this workshop as well as those you have used in your own classrooms.

Be creative! As you develop your ideas and put each one on a separate stickie, color coded, you will be able to share your ideas with others during the next activity.

When you are finished, and without talking, and as a group, place your stickies up on a big board.

Place them together by category/color.

Write each idea/best practice for your lesson plan on a stickie. Use a different color stickie for each kind of scaffolding.✎ concrete

kinestheticlinguisticgraphic organizers

What kind of supports would help English language learners to solve the problem without lowering its cognitive demand (telling them what do, telling them the answer?

BRAINSTORM

Read all of the stickies silently.

Get into groups of three.

In your groups, take a group of 4-5 stickies from any of the categories. Put them in the order you would use them in a lesson plan to teach the word problem to English language learners.

Copy one of the stickies to use in more than one grouping if needed.

Keep arranging and rearranging the stickies until the group feels they are in the order that best supports the learning of English language learners.


How could you take any four stickies, each from a different category, and put them in the order you would use them in a lesson for English language learners?

Lesson plans: Sequence of supporting strategies

for English language learners

GROUP Share your thoughts on the lesson plan with your group. •Why did we arrange the different parts of the lessons in this particular sequence?

•Are there any parts that need to be together; ie a language scaffold and a concrete activity?

•Do all parts of the lesson support English language learners in developing their own understanding?

•Do any tell them what to do? Do any tell them the answers? Can we think of alternatives that scaffold their learning but don’t tell them what to do or give them the answers?

Work as a group to modify the lesson.

Add any of the best practices used in the workshop that would support English language learners.


Count off by 3s in your group.

Look over Handout 16A,B, C and D, which discuss a number of ways to scaffold the lesson in each area. Some may be similar to those you have written, some may be new.

Assign #1 to read the language scaffolds

#2 to read the mathematical scaffolds

#3 to read the cultural scaffolds

What other supports can we use?

Choose one or two strategies or scaffolding ideas from the section you have read to share with your partners. Decide on a time each person will report back to the group. Share your selections in your group.

SHARE

1-16A,B,C,D

Put each part of the lesson on a different stickie, using a few words to describe the strategy.

Place the stickies in sequence.

SHAREAssign a presenter. As a group, help prepare that person explain how and why you developed the lesson in order to support English language learners in mastering high-level mathematics.


Post your sequence of lessons so that each group can see the work of all the groups.

Spread them out so that there is room for everyone to gather around each lesson. Take time to examine the lesson carefully.

GROUP A

GROUP B

GROUP A

Step 1. Presenter from Group A explains how each part of the lesson plan supports English language learners to learn the mathematical content without lowering the cognitive demand of the lesson.

Step 2. Everyone thinks of a follow-up question that will help the presenter expand on his/her response.

For example, call on all the #3s to ask the presenter a question:

Sample follow-up questions:Why do you think that strategy will work?What made you decide on the sequence of the lesson?In what ways does the lesson pay particular attention to the needs of English language learners?What contingencies are built into the lesson that do not lower the cognitive demand but recognize the misconceptions or problems students might have?

BEST PRACTICE:TUNING PROTOCOL• non-judgmental• encourages entire group to take responsibility for improving the lesson•presenter provides short overview• group examines the work• each person asks probing question: question designed not to provide a solution or critique but to encourage the presenters to expand upon and think more about their pedagogical decisions

GROUP A

Step 3. Each person, who is not in group A, gives one warm feedback - something they thought worked well in helping English language learners learn the mathematical concept of the lesson without lowering its cognitive demand.

Step 4. Each person, who is not in group A, gives one cool feedback - something they wonder about “I wonder if...” that might be considered in improving the lesson.

Step 5. One person from Group A tells the group one thing they learned from their feedback that could be used to improve the lesson.

Step 6. Each group presents, following the same sequence.

BEST PRACTICE:TUNING PROTOCOL (continued)• each person gives warm feedbak in rounds• each person gives cool feedback/suggesion in the form of “I wonder if...”• presenter(s) tells the group what they learned from the feedback that could improve the lesson.

GROUP A

GROUP B

What did you learn from creating the lesson plan for English language learners? from working with colleagues?

What did you learn from participating in the presentations and questioning?

METACOGNITIVE REFLECTION

WRITE

SHARE any part of your writing with a partner.

✎ 1-17

Teachers and Students Trying Out Best Practices



Using Handout 1-18, take notes on

Short videos of teachers and students

Video #2

1-18

Video #2: Same class as in earlier video

Urban classroom7th grade40% English language learners

Clip shows English language learners working in a small group and answering a question during a large group share out

Video #2

1-19A,B

PAIR Discuss with a partner



SHARE some of the responses you heard with the larger group.

Use same protocol THINK WRITE PAIR SHARE with each video.

Video#3

Urban classroomAll subjects taught in classroom7th and 8th grade100% English language learnersRecent immigrants to the United States

Experienced teacher of English language learners

Clip shows teacher providing directions to English language learners. This is the first time she is introducing this strategy.

1-20

Video #3

Video #4 Urban classroom7th grade100% English language learnersSecond year in ESL classroom

2nd year teacher of English language learners

Clip shows students using a vocabulary building exercise

1-21

Video #4

1-22

Using Best Practices in Our Classrooms

1-23

Collect evidence (student work, teacher lesson plans, video, audio, etc.) of how well it worked to bring to the next workshop.

Write down one strategy to try out with your own students.

PAIR with a partner to discuss the strategy.

1-24

“I chose the ____________strategy because....”

“What do you think will be your biggest challenge?”

I will collect evidence on how well it helped my students learn by ......................................”

“Why do you think that evidence will help you assess how well the strategy is working for you and your students?”

Workshop 1



Thank you for attending the workshop

Project Development Team

‣ Turning Points, Center for Collaborative Education Dr. Sara Freedman, Project Developer Dr. Dan Lynn Watt, Math Consultant

‣ Teachers, Burncoat School, Worcester Massachusetts Judith Murphy Tracy Olearczy

‣ Teachers, Calcutt School, Central Falls Rhode Island Cathy Carvalho Jennifer Martin Jillian O’Keefe

© Copyright 2009 Sara Freedman and Dan Watt for The Center for Collaborative Education/Turning Points